Divisibility Rule of 661

The divisibility rule for 661 is a method by which we can find out if a number is divisible by 661 or not without using the division method.

Check whether 1983 is divisible by 661 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 2, here in 1983, 3 is the last digit, so multiply it by 2. 3 × 2 = 6 

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 198–6 = 192.

Step 3: As it is shown that 192 is not a multiple of 661, the number is not divisible by 661. If the result from step 2 isn't a multiple of 661, then the number isn't divisible by 661.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 661. 

• Know the multiples of 661: Memorize the multiples of 661 (661, 1322, 1983, 2644, 3305…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 661, then the number is divisible by 661.
   
• Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 661.
  
   For example: Check if 5943 is divisible by 661 using the divisibility test.Multiply the last digit by 2, i.e., 3 × 2 = 6Subtract the remaining digits excluding the last digit by 6, 594–6 = 588 
  
  Still, 588 is a large number, hence we will repeat the process again and multiply the last digit by 2, 8 × 2 = 16. 
  
  Now subtracting 16 from the remaining numbers excluding the last digit, 58–16 = 42
  
  As 42 is not a multiple of 661, 5943 is not divisible by 661.
   
• Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 661 if the final result after applying the rule is a multiple of 661.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 661 are 661, 1322, 1983, 2644, etc.
   
• Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
   
• Verification: Verification is the process of confirming a result, often using a different method like direct division to check if a number is divisible by another.